It's best to answer this as purely an SQL question, which it is. You need to assign a table alias when joining the same table two or more times.
You seem to only be assigning aliases to the column. To assign an alias to a column or table, you can add the alias directly after the column or table name (AS can also be used but isn't necessary for MySQL)
A common thing is to number the tables as t1, t2, t3, etc.
SELECT t1.name name1, t2.name name2 FROM ... INNER JOIN team_table t1 ON ... INNER JOIN team_table t2 ON ...
This aliases the first join as t1 and the second join as t2, which you would use when accessing data from that specific join (SELECT t1.name).